The present age of Jason is given as 10 years.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given problem can be solved as follows,
Suppose the age of Jason 6 years ago was x.
Then, the age of Annabelle 6 years ago was 2x.
Their present ages are x + 6 and 2x + 6 years respectively.
As per the question, the following equation can be formed as follows,
2x + 6 = x + 6 + 4
=> 2x - x = 10 - 6
=> x = 4
Thus the present age of Jason is 4 + 6 = 10 years.
Hence, the age of Jason now is 10 years.
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Find the Mean Median Mode and range of each data set that is obtained after adding the given constant. 12,10,15,17,15,9,10,15,12,14,+9. Please show work.
Mean: 12.545454545455
Median: 12
Range: 8
Mode: 15, appeared 3 times
Largest: 17
Smallest: 9
Sum: 138
Count: 11
what is 3 ^9? how to solve?
Tourists covered 255 km for a 4-hour ride by car and a 7-hour ride by train. What is the speed of the train, if it is 5 km/h greater than the speed of the car?
[tex]\\ \text{Let the speed of the car is x km/h}\\ \text{Then, the speed of the train is x+5 km/hr}\\ \text{Now, 4 hr is the time of the car}\\ \text{and 7 hour is the time of the train}\\ \text{We know the formula}\\ \text{Distance }= \text{Velocity }\times \text{ time}\\ \text{Distance travelled by car is 4x}\\ \text{Distance travelled by train is }7(x+5)\\ \text{The total distance is given by 255 km. Hence, we have}\\ 4x+7(x+5)=255\\ 4x+7x+35=255\\ 11x=220\\ x=20[/tex]
The speed of the car is 20 km/hr and hence the speed of the train is 2+5=25 km/hr.
The speed of the train is given by 25 km/hr.
If a scare as side lengths of 5 inches what is the lengths of the diagonal to the nearest 10th of in inch
My coin collection had 27 coins. They are only quarters and half-dollars. If its worth $10.50. How many are there of each coin?
PLEASE SHOW WORK
fatima wants to find the value of sin theta, given cot theta equals 4/7. which identity would be best for fatima to use?
Answer:
D edge
Step-by-step explanation:
Add (13a + 5b) + (a + 5b - 3)
Mary is walking 3 miles per hour jerry starts jogging at a rate of 4 miles per hour after marry has been walking for 15 minuets jerry jogs 2 miles as Mary continues walking and they both stop at the same time
HELP!! Drag values to complete each equation.
Answer:
a.[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
Step-by-step explanation:
We have to complete each equation
We are given that
[tex]((12)^2)^3\cdot (12)^{-4}[/tex]
[tex](12)^6\cdot (12)^{-4}[/tex]
Using identity
[tex](a^x)^y=a^{xy}[/tex]
[tex](12)^{6-4}=(12)^2[/tex]
Using identity: [tex]a^x\cdot a^y=a^{x+y}[/tex]
[tex]((12)^2)^3\cdot (12)^{-4}=12^2[/tex]
b.[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}[/tex]
[tex]\frac{(12)^2}{(12)^2}[/tex]
[tex](12)^{2-2}=(12)^0=1[/tex]
Using identity: [tex]\frac{a^x}{a^y}=a^{x-y},a^0=1[/tex]
[tex]\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1[/tex]
Parallel lines r and s are cut by two transversals, parallel lines t and u.
Which angles are alternate exterior angles with angle 11?
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
Two angles are called Alternate exterior angles if
1. They are on the exterior side of parallel lines and
2. Lie on the opposite sides of the transversal line.
It is given that
[tex]r\parallel s[/tex] and [tex]t\parallel u[/tex]
From the figure it is noticed that the angle 13 and angle 5 are on the exterior side of parallel lines and they lie on the opposite sides of the transversal line.
Therefore alternate exterior angles with angle 11 are angle 13 and angle 5.
Answer:
The alternate exterior angles with angle 11 are angle 13 and angle 5.
Step-by-step explanation:
how do you do 27?????
what is 3√27x^9
3x^6
3x^3
9x^3
9x^6
The value of the expression ∛27x⁹ is 9x³.
The given expression is ∛27x⁹.
Cube root of twenty seven times of x power nine.
We can split the terms inside the cube root.
27=3×3×3
∛x⁹ = x³
Now let us plug in the above expression.
= 3√3³ × x⁹
= 3√3³ × √ x⁹
= 3 × 3 × x³
= 9x³.
Hence, the value of the expression ∛27x⁹ is 9x³.
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Find the surface area 4cm 5cm 6cm 13cm
the probability of winning the game is 7/10. What is the probability that they will lose?
The probability of losing the game is 3/10 or 0.3 when the probability of winning is 7/10, because the total probability must always equal 1.
If the probability of winning the game is 7/10, then the probability of losing the game is the complement of the probability of winning. This means we subtract the probability of winning from 1. Therefore, the probability of losing the game is 1 - 7/10 = 3/10 or 0.3. This is because the sum of the probabilities of all possible outcomes in a probability distribution must equal 1.
Which equation in point-slope form contains the point (4, –1) and has slope 3? y – 1 = 3(x + 4) y – 4 = 3(x + 1) y + 1 = 3(x – 4)
Answer:
the answer is option d y+1 =3 (x-4)
help! I will give thanks!
Roman saves $500 each year in account earning interest at an account earning interest at an annual rate of 4% compounded annually.How much interest will the account earn at the end of each of the first 3 years?
Karen is considering taking out a 20-year loan with monthly payments of $260 at an APR of 5.5%, compounded monthly, and this equates to a loan of $37,796.89. Assuming that the APR and the length of the loan remain fixed, which of these is a correct statement?
The correct statement is A;If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
How to calculate EMI?The EMI formula is :
[tex]\dfrac{pr(1 + r)^n}{(1 + r)^n - 1}[/tex]
Where r = 5.5/12/100 = 0.00425
p = 37,796.89
and n = 20 x 12 = 240
Putting the values in formula we get'
= (37,796.89x 0.00425 x 2.767)/1.767
= $350
Hence,
The correct statement is A; If Karen monthly payment $260 the amt of the loan that he is considering taking out would be less than $37,796.89
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Answer:If Karen's monthly payment were $240, the amount of the loan that she is considering taking out would be less than $37,796.89.
Step-by-step explanation:
The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of the external angles of a triangle. Which pair of angle measures was calculated?
The Exterior Angle Theorem establishes that the measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so
the answer is the option
A. the remote interior angles
simplify the problem sqrt 245c^5
Answer: the answer above is pretty much right, the answe is B
The vertex angle of an isosceles triangle is 20° less than the sum of the base angles. Which system of equations can be used to find the measure of the vertex and base angles?
A)
v + 2b = 180; 2b - 20 = v
B)
v + 2b = 180; 2b + 20 = v
C)
v - 2b = 180; v + 2b = -20
D)
v - 2b = 180; -2b - 20 = v
The answer to the above question can be explained as under -
We know that, the sum of angles of triangle is 180°.
So, vertex angle plus base angles are equal are equal to 180°.
Let the vertex angle be represented by "v" and base angles be represented by "b".
Thus, v + b + b = 180°
So, v + 2b = 180°
Next, the question says, the vertex angle is 20° less than the sum of base angles.
Thus, 2b - 20° = v
Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v
The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.
The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:
The sum of the angles in a triangle is 180°, leading to the equation: v + 2b = 180.The vertex angle v is 20° less than the sum of the base angles, giving us the equation: 2b - 20 = v.To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.
What is grater 9km or 145cm
9km is greater than 145cm due to the conversion factor between kilometers and centimeters.
9km is greater than 145cm because when comparing the two, you need to ensure they are in the same unit. To compare, convert km to cm, 9km = 9,000,000cm. So, 9,000,000cm is greater than 145cm.
If you buy a computer directly from the manufacturer for $ 2,469 and agree to repay it in 48 equal installments at 2.1 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Final answer:
The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.
Explanation:
To calculate the monthly payments, you can use the formula for the monthly payment on a loan:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P is the monthly paymentr is the monthly interest ratePV is the present value or the loan amountn is the total number of paymentsUsing the given values, we can calculate:
P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)
P ≈ $61.02
Therefore, the monthly payments would be approximately $61.02.
To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:
Total Interest = (P * n) - PV
Total Interest ≈ ($61.02 * 48) - $2469
Total Interest ≈ $1704.96 - $2469
Total Interest ≈ -$764.04
Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.
A fair dice is rolled 5 times in sequence. what is the probability that you will get exactly the same number for all 5 rollings
Find the variable of each pair
The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.
A.26.5cm3
B.44.2cm3
C.79.5cm3
D.132.5cm3
Will give brainliest! Which are simplified forms of the expression sec^2theta sin2theta
Which is the second answer? I already got the first one
Answer:
C) 2 tan θ
E) [tex]\frac{sin2[theta]}{cos^2[theta]}[/tex] (it wouldn't let me do the actual θ symbol)
Step-by-step explanation:
This is essentially what the other person said, but in a better format.
A cube has a side length of 120 cm, what is its volume in cubic meters? (100 cm = 1 m)
The value of volume of cube is,
⇒ V = 1.728 meter³
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
A cube has a side length of 120 cm.
Since, We know that;
1 m = 100 cm
Hence,
120 cm = 120 / 100 m
= 1.2 m
So, Volume of cube is,
⇒ V = side³
⇒ V = 1.2³
⇒ V = 1.728 meter³
Thus, volume of cube is,
⇒ V = 1.728 meter³
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which of the points satisfy the linear inequality graphed here?
a) (0,0)
b) (10,0)
c) (-10,0)
d) (10,10)
Which graph would help solve the equation 5log(x+3)=5
The value of x is 7 for the given equation.
What is logarithm?Logarithm, a mathematical concept involving multiplication. It is the exponent or power to which a base must be raised to yield a given number.
For the given situation,
The equation is 5log(x+3)=5.
On solving this equation, we can get value of x.
⇒ [tex]5log(x+3)=5[/tex]
⇒ [tex]log(x+3)=1[/tex]
We know that, log 10 = 1
Then,
⇒ [tex]log(x+3)=log10[/tex]
⇒ [tex]x+3=10[/tex]
⇒ [tex]x=7[/tex]
Hence we can conclude that the value of x is 7 and the graph fro the logarithmic equation is shown below.
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